Lorentz Violation and Synchrotron Radiation

TL;DR

This paper investigates how a specific type of Lorentz violation affects synchrotron radiation from ultrarelativistic particles, deriving exact trajectories and setting bounds on Lorentz-violating coefficients using astrophysical data.

Contribution

It provides an exact solution for particle trajectories under Lorentz violation and derives observational bounds from Crab nebula data.

Findings

Particle trajectories are noncircular and nonperpendicular to magnetic fields due to Lorentz violation.

The radiation spectrum shows directional dependence caused by Lorentz-violating effects.

A bound on Lorentz-violating coefficients is established at the level of 6×10^{-20} using astrophysical observations.

Abstract

We consider the radiation emitted by an ultrarelativistic charged particle moving in a magnetic field, in the presence of an additional Lorentz-violating interaction. In contrast with prior work, we treat a form of Lorentz violation that is represented by a renormalizable operator. Neglecting the radiative reaction force, the particle's trajectory can be determined exactly. The resulting orbit is generally noncircular and does not lie in the place perpendicular to the magnetic field. We do not consider any Lorentz violation in the electromagnetic sector, so the radiation from the accelerated charge can be determined by standard means, and the radiation spectrum will exhibit a Lorentz-violating directional dependence. Using data on emission from the Crab nebula, we can set a bound on a particular combination of Lorentz-violating coefficients at the $6\times10^{-20}$ level.